Yes you can be no dig without being organic. Healthy soil is indeed the best goal for all of us.
Organic is not a precise term anyway, it has altered quite a bit in the thirty years I have been growing organically.
In my earlier post I was concerned by your reference to ‘one more dose’ with slug pellets, in a general way rather than for specific plants, and pointed out that, when used, they can be applied individually, near tender plants when they are vulnerable.